Similarity principle based multi-physical parameter unification and comparison in salinity-gradient osmotic energy conversion

Nanofluidic osmotic energy conversion has the potential of directly converting renewable salinity-gradient energy into electricity. Existing research mainly focuses on the ion selectivity and robustness of nanoporous membranes. However, the multi-physical governing parameters of salinity-gradient osmotic energy conversion have never been unified and compared. In the current study, a similarity principle is constructed for ion selective transport in nanofluidic channel through dimensionless analysis, which lays a theoretical foundation for experimental design and data analysis to develop engineering correlations in osmotic energy conversion under a salinity-gradient. The derived dimensionless governing parameters are grouped into four categories with different physical meanings including ion driving source, ion selectivity, ion transport characteristics, and nanoporous membrane configuration. Particularly, a key dimensionless governing parameter named "IonS " is developed for ion selectivity of nanofluidic channel, indicating that the ion selectivity has a positive linear correlation with the nanochannel surface charge density and a negative linear correlation with ion concentration and nanofluidic channel radius. Considering the similarity phenomena in salinity-gradient osmotic energy conversion, future experimental burden is dramatically alleviated. In addition, a sensitivity analysis using Taguchi method is carried out to evaluate the dominance order of multi-physical parameters in salinity-gradient osmotic energy conversion. The ion concentration and nanofluidic channel radius are found to be dominant for maximum output power and energy conversion efficiency because of their significant influences on the thickness of electric double layer and its overlapping degree. The current dimensionless analysis based similarity principle and sensitivity analysis of multi-physical parameters offer an intrinsic insight for ion selective transport in nanofluidic channels, contributing to the development of salinity-gradient osmotic energy conversion for practical applications.